Regarding the prophecy of Jesus (peace be with him), we can read the below verse in the Quran:  

وَإِذْ قَالَ عِيسَى ابْنُ مَرْيَمَ يَا بَنِي إِسْرَائِيلَ إِنِّي رَسُولُ اللَّهِ إِلَيْكُم مُّصَدِّقًا لِّمَا بَيْنَ يَدَيَّ مِنَ التَّوْرَاةِ وَمُبَشِّرًا بِرَسُولٍ يَأْتِي مِن بَعْدِي اسْمُهُ أَحْمَدُ فَلَمَّا جَاءهُم بِالْبَيِّنَاتِ قَالُوا هَذَا سِحْرٌ مُّبِينٌ ﴿٦﴾

And remember, Jesus, the son of Mary, said: "O Children of Israel! I am the apostle of Allah (sent) to you, confirming the Law (which came) before me, and giving Glad Tidings of a Messenger to come after me, whose name shall be Ahmad." But when he came to them with Clear Signs, they said, "this is evident sorcery!" (Quran 61:6)

The mission of Jesus was to his own people, the Jews. Cf. Matt. 10:5-6. See also Matt. 15:24: "I am not sent but to the lost sheep of Israel;" also Matt. 15:26: "It is not meet to take the children's bread, and to cast it to dogs."
"Ahmad", or "Muhammad", the Praised One, is almost a translation of the Greek word Periclytos. In the present Gospel of John. 14:16, 15:26, and 16:7, the word "Comforter" in the English version is for the Greek word "Paracletos", which means "Advocate", "one called to the help of another, a kind friend", rather than "Comforter". Our doctors contend that Paracletos is a corrupt reading for Periclytos, and that in their original saying of Jesus there was a prophecy of our holy Prophet Ahmad by name. Even if we read Paraclete, it would apply to the holy Prophet, who is "a Mercy for all creatures" (21:107) and "most kind and merciful to the Believers" (9:128).

Let’s see how many times are the names of different prophets mentioned in the Quran:

Musa (Moses) mentioned 136 times
Ibrahim (Abraham) – 69 times
Nuh (Noah) – 43 times
Lut (Lot) 27 times
Yusof (Joseph) 27 times
Isa (Jesus) – 25 times
Adam 25 times
Harun (Aaron) 20 times
Sulayman (Solomon) 17 times
Ishaq (isaac) 17 times
Dawud (David) 16 times
Yaqub (Jacob) 16 times
Ismael (Ishmael) 12 times
Shuayb 11 times
Salih 9 times
Zakaria 7 times
Hud 7 times
Yahya 5 times
Muhammad 4 times

They are all Muslims, who surrendered themselves under the will of the One God. This is what Quran means about Islam and not the Shihada (oath for accepting God). The Muslim existence today is related to birth or the acceptance of faith therefore it has different meaning comparing to Quran where terminology of Muslim is applied to Mohammed (PBUH) and the Prophets before him. After the death of Mohammed, the age of revelations finished and the age of Prophets came to end as well. Even the line of Muslims who got guidance from Allah finished, too. After Mohammed (PBUH) the existence of Muslims has changed. A today Muslim can be follower, ignoring, practicing literally, interpreting subjectively and thousands of other versions. Therefore, if a Muslim today is asked about the teachings of Islam, he will give an answer of a Muslim today in the light of his subjective comprehension. There is a chance to ask Muslims in the age of Prophecies as well: it happens while reading Quran. The answer is there in every line.